IMathAS-libretexts

Test the claim that the proportion of men who own cats is smaller than 40% at the 0.05 significance level.

The null and alternative hypothesis would be:

\displaystyle {H}_{{0}}:{p}={0.4}

\displaystyle {H}_{{1}}:{p}\ne{0.4}

\displaystyle {H}_{{0}}:{p}\le{0.4}

\displaystyle {H}_{{1}}:{p}>{0.4}

\displaystyle {H}_{{0}}:\mu={0.4}

\displaystyle {H}_{{1}}:\mu\ne{0.4}

\displaystyle {H}_{{0}}:\mu\ge{0.4}

\displaystyle {H}_{{1}}:\mu<{0.4}

\displaystyle {H}_{{0}}:\mu\le{0.4}

\displaystyle {H}_{{1}}:\mu>{0.4}

\displaystyle {H}_{{0}}:{p}\ge{0.4}

\displaystyle {H}_{{1}}:{p}<{0.4}

The test is:

two-tailed

right-tailed

left-tailed

Based on a sample of 300 people, 39% owned cats

The test statistic is: (to 2 decimals)

The critical value is: (to 2 decimals)

Based on this we:

Reject the null hypothesis
Fail to reject the null hypothesis

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